• Journal of Korean Institute of Industrial Engineers
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• v.27 no.3
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• pp.250-259
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• 2001

Given a tree structured network in which each node has its own demand and also stands for a candidate location of a potential facility, such as plant or warehouse, a capacitated facility location problem on the network (CFLPOT) is to decide capacitated facility locations so that the total demand occurred on the network can be satisfied from those facilities with the minimum cost. In this paper, we first introduce a mixed integer programming formulation for CFLPOT with two additional assumptions, the indivisible demand assumption and the contiguity assumption and then show that it can be reformulated as a tree partitioning problem with an exponential number of variables. We then show that it can be solved in O($n^2b$) time by utilizing the limited column generation method developed by Shaw (1993), where n is the total number of nodes in the network and b is the maximum facility capacity. We also develop a depth-first dynamic programming algorithm with a running time of O(nb) for finding the locally maximal reduced cost which plays an important role in the limited column generation method. Finally, we implement our algorithms on a set of randomly generated problems and report the computational results.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.10
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• pp.5244-5259
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• 2019

With the continuous development of LBS (Location Based Service) applications, privacy protection has become an urgent problem to be solved. Differential privacy technology is based on strict mathematical theory that provides strong privacy guarantees where it supposes that the attacker has the worst-case background knowledge and that knowledge has been applied to different research directions such as data query, release, and mining. The difficulty of this research is how to ensure data availability while protecting privacy. Spatial multidimensional data are usually released by partitioning the domain into disjointed subsets, then generating a hierarchical index. The traditional data-dependent partition methods need to allocate a part of the privacy budgets for the partitioning process and split the budget among all the steps, which is inefficient. To address such issues, a novel two-step partition algorithm is proposed. First, we partition the original dataset into fixed grids, inject noise and synthesize a dataset according to the noisy count. Second, we perform IH-Tree (Improved H-Tree) partition on the synthetic dataset and use the resulting partition keys to split the original dataset. The algorithm can save the privacy budget allocated to the partitioning process and obtain a more accurate release. The algorithm has been tested on three real-world datasets and compares the accuracy with the state-of-the-art algorithms. The experimental results show that the relative errors of the range query are considerably reduced, especially on the large scale dataset.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.34C no.2
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• pp.38-49
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• 1997

In this paper, w describe partitioning large circuits into multiple chips on the programmable FPCB for rapid prototyping. FPCBs consists of areas for FPGAs for logic and interconnect components, and the routing topology among them are predetermined. In the partition problem for FPCBs, the number of wires ofr routing among chips is fixed, which is an additonal constraints to the conventional partition problem. In order to deal with such aconstraint properly we first define a new partition problem, so called the topologybased partition problem, and then propose a heuristic method. The heuristic method is based on the simulated annealing and clustering technique. The multi-level tree clustering technique is used to obtain faster and better prtition results. In the experimental results for several test circuits, the restrictions for FPCB were all satisfied and the needed execution time was about twice the modified K-way partition method for large circuits.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.4
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• pp.394-405
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• 2001

Since most real-world application data involve continuous-valued attributes, properly addressing the discretization process for constructing a decision tree is an important problem. A continuous-valued attribute is typically discretized during decision tree generation by partitioning its range into two intervals recursively. In this paper, by removing the restriction to the binary discretization, we present a hybrid multi-interval discretization algorithm for discretizing the range of continuous-valued attribute into multiple intervals. On the basis of experiment using semiconductor etching machine, it has been verified that our discretization algorithm constructs a more efficient incremental decision tree compared to previously proposed discretization algorithms.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.330-333
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• 2003

Initial cluster size for clustering of partitioning methods is very important to the clustering result. In K-means algorithm, the result of cluster analysis becomes different with optimal cluster size K. Usually, the initial cluster size is determined by prior and subjective information. Sometimes this may not be optimal. Now, more objective method is needed to solve this problem. In our research, we propose a hybrid genetic algorithm, a tree induction based evolution algorithm, for determination of optimal cluster size. Initial population of this algorithm is determined by the number of terminal nodes of tree induction. From the initial population based on decision tree, our optimal cluster size is generated. The fitness function of ours is defined an inverse of dissimilarity measure. And the bagging approach is used for saying computational time cost.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.33A no.11
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• pp.128-139
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• 1996

In this paper, we propose an algorithm to solve the problem of placement of rectangular blocks whose sizes and shpaes are pre-determined. The proposed method solves the placement of many retangular blocks of different sizes and shapes in a hierarchical manner, so as to minimize the chip area. The placement problem is divided into several sub-problems: hierarchical partioning, hierarchical area/shape estimation, hierarchical pattern pacement, overlap removal, and module rotation. After the circuit is recursively partitioned to build a hierarchy tree, the necessary wiring area and module shpaes are estimated using the resutls of the partitioning and the pin information before the placement is performed. The placement templaes are defined to represent the relative positions of the modules. The area and the connectivity are optimized separately at each level of hierachy using the placement templates, so the minimization of chip area and wire length can be achieved in a short execution time. Experiments are made on the MCNC building block benchmark circuits and the results are compared with those of other published methods. The proposed technique is shown to produce good figures in tems of execution time and chip area.

• Journal of the Korea Society of Computer and Information
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• v.3 no.4
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• pp.63-69
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• 1998

The area optimization of the power distribution network is an important problem in the layout design of VLSI systems. In this paper we propose noval methods to solve the problem of designing minimal area power distribution nets, while satisfying voltage drop and electromigration constraints. We propose two novel greedy heuristics for power net design-one based on bottom-up tree construction using greedy merging and the other based on top-down linearly separable partitioning.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.2
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• pp.29-46
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• 1998

In this paper, we develop detailed algorithms for implementing the so-called Limited Column Generation procedure for Local Access Telecommunication Network(LATN) design problem. We formulate the problem into a tree-partitioning problem with an exponential number of variables. Its linear programming relaxation has all integral vertices, and can be solved by the Limited Column Generation procedure in just n pivots, where n is the number of nodes in the network. Prior to each pivot. an entering variable is selected by detecting the Locally Most Violated(LMV) reduced cost, which can be obtained by solving a subproblem in pseudo-polynomial time. A critical step in the Limited Column Generation is to find all the LMV reduced costs. As dual variables are updated at each pivot, the reduced costs have to be computed in an on-line fashion. An efficient implementation is developed to execute such a task so that the LATN design problem can be solved in O(n$^2$H), where H is the maximum concentrator capacity. Our computational experiments indicate that our algorithm delivers an outstanding performance. For instance, the LATN design problem with n＝150 and H＝1000 can be solved in approximately 67 seconds on a SUN SPARC 1000 workstation.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.04a
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• pp.54-68
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• 1995

In this paper, we develop detailed algorithms for implementing the so-called Limited Column Generation procedure for Local Access Telecommunication Network (LATN) Design problem. We formulate the problem into a tree-partitioning problem with an exponential number of variables. Its linear programming relaxation has all integral vertices, and can be solved by the Limited Column. Generation procedure in just n pivots, where n is the number of nodes in the network. Prior to each pivot, an entering variable is selected by detecting the Locally Most Violated (LMV) reduced cost, which can be obtained by solving a subproblem in pseudo-polynomial time. A critical step in the Limited Column Generation is to find all the LMV reduced costs. As dual variables are updated at each pivot, the reduced costs have to be computed in an on-line fashion. An efficient implementation is developed to execute such a task so that the LATN Design problem can be solved in O(n$^{2}$H), where H is the maximum concentrator capacity. Our computational experiments indicate that our algorithm delivers an outstanding performance. For instance, the LATN Design problem with n = 150 and H = 1000 can be solved in approximately 67 seconds on a SUN SPARC 1000 workstation.

• Journal of the Korea Computer Graphics Society
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• v.5 no.2
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• pp.9-23
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• 1999

Visibility preprocessing is a useful method to reduce the complexity of scenes to be processed in real-time, and so enhances the overall rendering performance for interactive visualization of virtual environments. In this paper, we propose an efficient visibility preprocessing method. In the proposed method, we assume that navigatable areas in virtual environments are partitioned into rectangular parallelpiped cells or sub-worlds. To preprocess the visibility of each polygon for a given partitioned cell, we should determine at least the area-to-area visibility. This is inherently a four-dimensional problem. We efficiently express four-dimensional visibility information on two-dimensional spaces and keep it within a ternary tree, which is conceptually similar to a BSP(Binary Space Partitioning) tree, by exploiting the characteristics of conservative visibility. The proposed method is able to efficiently handle more general environments like urban scenes, and remove invisible polygons jointly blocked by multiple occluders. The proposed method requires O(nm) time and O(n+m) space. By selecting a suitable value for m, users can select a suitable level of trade-off between the preprocessing time and the quality of the computational result.